Question: Divide the polynomials.
Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. $\begin{array}{r} x-\phantom{1}4 \\ x-5|\overline{x^2-9x+14} \\ \mathllap{-(}\underline{x^2-5x\phantom{+14}\rlap )} \\ -4x+14 \\ \mathllap{-(}\underline{-4x+20\rlap )} \\ -6 \end{array}$ We get that the quotient is $x-4$ and the remainder is $-6$, and therefore: $\dfrac{x^2-9x+14}{x-5}=x-4-\dfrac{6}{x-5}$ [I want to see a different way of performing the division.]